How important is it that the generator of a generative adversarial network doesn't take in information about input classes?
If you're building a straight "vanilla" generative adversarial network, it's best to understand the network as a statistical engine:  You are training the generator on samples of a statistical distribution.  (And you're training the discriminator to distinguish between "ground truth" images, and images from that generator.)

Once you replace the input noise with another image... well.  Strictly speaking, it is probably still a generative adversarial network, if you're still doing everything else the same.  It is still a generator and a discriminator, acting in an adversarial fashion. 

But you've radically altered the input distribution, so there is a good chance that you're no longer accomplishing what you want to accomplish unless you're being very careful and clever. 

That said, there are GAN variants which do take images rather than noise as inputs.  See the wonderful paper on CycleGANs by Zhu, et al, along with a substantial body of followup literature. And note that CycleGANs use not one, but two discriminators, so even here the discriminator is necessary.